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tg15∘⋅tg25∘⋅tg35∘⋅tg85∘tg15∘⋅tg25∘⋅tg35∘⋅tg85∘=?

Guest Mar 27, 2017
 #1
avatar+19653 
+1

tg15∘⋅tg25∘⋅tg35∘⋅tg85∘tg15∘⋅tg25∘⋅tg35∘⋅tg85∘=?

 

\(\tan(15°)\cdot \tan(25°)\cdot \tan(35°)\cdot \tan(85°)=1 \)

 

\(\tan(15°)\cdot \tan(25°)\cdot \tan(35°)\cdot \tan(85°)\times \tan(15°)\cdot \tan(25°)\cdot \tan(35°)\cdot \tan(85°) =1\times 1 = 1 \)

 

laugh

heureka  Mar 28, 2017
edited by heureka  Mar 28, 2017
 #2
avatar+92806 
0

 

Could you expand on your answer please Heureka?

 

How do you know that that product is 1?

 I asssume you did not use a calculator ?

Melody  Mar 28, 2017
 #3
avatar
0

tan(15°) tan(25°) tan(35°) tan(85°) =(2 - sqrt(3)) tan((5 π)/36) tan((7 π)/36) cot(π/36)(Radians) =1

Guest Mar 28, 2017

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